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Calculus and Optimization for Machine Learning
Week 5
Practice Quiz #1

Practice QuizPractice Quiz • 30 min30 minutes

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Practice Quiz #1

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Practice Quiz #1

Total points 4

1.

Question 1

Choose the incorrect statement:

1 / 1 point

$\int \frac{x dx}{1+x^2}=\ln 2\sqrt{1+x^2} +C$

$\int f(x)dx=\int f(x) d(x+1)$

$\int e^x \cdot \cos x dx=\left(\int e^x dx\right) \cdot \left( \int \cos x dx \right)=e^x\sin x+C$

Correct

That's a nightmare, you are right!

2.

Question 2

Find the indefinite integral $\int \ln x dx$ . Write the antiderivative $F(x)$ such as $F(e)=0$ .

1 / 1 point

x \log{\left (x \right )} - x

x*ln(x)-x

Correct

Correct!

3.

Question 3

Find the indefinite integral $\int x(1-x^2)^5 dx$ . Assume that we are only interested in the antiderivative $F(x)$ such as $F(1)=0$ . Write the coefficient of the largest power of $x$ in produced polynomial.

1 / 1 point

- \frac{1}{12}

-1/12

Correct

Correct!

4.

Question 4

Find the antiderivative of $\int \frac{dx}{x(x+2)}$ that approaches $0$ as $x \to +\infty$ . Write the sum of all roots of the produced function.

If there are no roots, write $-1$ .

1 / 1 point

-1

-1

Correct

Correct!